Design and evaluation of digital signal processing algorithms for acoustic feedback and echo cancellation

This thesis deals with several open problems in acoustic echo cancellation and acoustic feedback control. Our main goal has been to develop solutions that provide a high performance and sound quality, and behave in a robust way in realistic conditions. This can be achieved by departing from the traditional ad-hoc methods, and instead deriving theoretically well-founded solutions, based on results from parameter estimation and system identification. In the development of these solutions, the computational efficiency has permanently been taken into account as a design constraint, in that the complexity increase compared to the state-of-the-art solutions should not exceed 50 % of the original complexity. In the context of acoustic echo cancellation, we have investigated the problems of double-talk robustness, acoustic echo path undermodeling, and poor excitation. The two former problems have been tackled by including adaptive decorrelation filters in the adaptive filtering algorithm, with the aim of whitening the near-end signal component and the residual echo component resulting from undermodeling. These decorrelation filters can be identified concurrently with the acoustic echo path by using the prediction error method (PEM) for system identification. As a result, a 30-40 dB misadjustment improvement (in the double-talk case) and a 20-35 dB variance decrease (in the undermodeling case) have been obtained, at the cost of a complexity increase of 50 % compared to the normalized least mean squares (NLMS) algorithm. The poor excitation problem has been approached from a Bayesian minimum mean square error (MMSE) point of view. This approach has led to the use of a regularization matrix different from the traditional scaled identity matrix, which may incorporate prior knowledge on the acoustic echo path. It has moreover been shown that the existing proportionate adaptation algorithms can be viewed as a special case of the proposed approach to regularization. A misadjustment improvement up to 10 dB has been obtained with a regularized NLMS-type algorithm that requires only 25 % more computations than the original NLMS algorithm. Two approaches to acoustic feedback control have been considered in this thesis, namely notch-filter-based howling suppression (NHS) and adaptive feedback cancellation (AFC). In the context of NHS, we have developed a novel parametric frequency estimation method, which is characterized by a computational complexity that is linear in the data record length. Also, a new design procedure for biquadratic parametric equalizer filters is proposed, based on a technique known as pole-zero placement. In the context of AFC, the PEM-based AFC approach that was proposed earlier for hearing aid AFC has been generalized to room acoustic and audio applications. The PEM-based approach relies on the identification of a near-end signal model that can be used in the design of decorrelating prefilters. These prefilters are aimed at resolving the AFC closed-loop signal correlation problem and hence providing an unbiased acoustic feedback path model. We have obtained a misadjustment improvement of 7 dB compared to the hearing aid PEM-based AFC algorithm and of 12 dB compared to the NLMS algorithm, at the cost of a 25-50 % complexity increase compared to NLMS. In a comparative evaluation with the state-of-the-art acoustic feedback control methods, the PEM-based AFC approach was shown to outperform the existing phase-modulating feedback control (PFC) and NHS methods, as well as the AFC methods that apply a decorrelation in the closed signal loop, in terms of the achievable maximum stable gain and sound quality, both for speech and audio signals.